Heard this asked so many times so im going to run through it all. You will need a pokemon with strength and surf for this.

Step 1: Defeat the Elite Four

Step 2: Fly or boat (via Vermillion) to island one.

Step 3: Go inside the pokecenter and talk to Celio by the big machine

Step 4: He will mention something about a Ruby, at this point you need to go to MT. Ember (also on island one)

Step 5: Defeat the team rocket guys off to the right of the entrance to MT. Ember

Step 6: Enter the cave and follow the path through

Step 7: Complete the first 2 rock puzzles, at the split road take the one to the left and follow through until the Ruby

Step 8: The pathway to the right is a faster way out the cave

Step 9: Fly (or walk) back to Celio with the Ruby in hand. He will upgrade your ferry pass to allow full access to the other islands.

Enjoy!

As per a CM request here is another guide with directions on how to get the Sapphire.

You will need a pokemon with Surf and one that can learn Waterfall for step 1. After step one you must have a pokemon that knowsCut and Strength

Step 1: You must defeat the Rocket Grunts inside Icefall cave (island 4). To do this you must first complete the Ice Puzzle and obtain HM Waterfall at the end of the cave. Once obtained return to the front of the cave and use Waterfall on the Waterfall (duh)

Step 1.5: Head to island 5

Step 2: Go to Five island Meadow and defeat the Rockets outside the Warehouse to obtain the first password

Step 3: Fly/Boat to island 6

Step 4: Head out East from the Pokecenter and Bike/Walk south

Step 5: Follow the path until you reach Ruin Valley

Step 6: At Ruin Valley take left path and follow it through, the two paths that require strength lead to HP UP and a Full Restore

Step 7: After following the left path you should reach a small closed cave. The door should have Braille on it